Hello everyone,

I am looking for a fast algorithm which enumerates 16-bit integers, sorted by the number of bits that are set. I have come up with one of my own, but I am wondering if there is a faster, better way of doing this.

Ideally, the numbers with the same number of set bits should be sorted (ascending or descending), but that isn't a must.

Simplified to 4 bits, the output sequence could look like this:

1111b,
0111b, 1011b, 1101b, 1110b,
0011b, 0101b, 0110b, 1001b, 1010b, 1100b,
0001b, 0010b, 0100b, 1000b,
0000b